C.2 · IB Physics
Transverse and longitudinal waves
The same travelling wave carried by a row of particles in two ways. Transverse particles oscillate at right angles to the direction of travel; longitudinal particles oscillate along it, forming compressions and rarefactions. Follow the highlighted particle: it only oscillates about its own equilibrium position.
Predict first
Start from the defaults (f = 0.50 Hz, v = 1.0 m s⁻¹, λ = 2 m). You raise the frequency to 1.00 Hz without changing the wave speed. What happens to the wavelength?
The speed is fixed, so λ = v ÷ f. Doubling f halves λ: 1.0 ÷ 1.00 = 1 m. The waves are produced twice as often but travel at the same speed, so they are closer together.
Check it in the model: Move the Frequency, f slider from 0.50 to 1.00 Hz and read the Wavelength λ line.
highlighted particle compression (C) rarefaction (R) and particles
v = fλ, T = 1 ÷ f
maximum particle speed = 2πfA
phase lag at x = 360° × x ÷ λ
Try this
- Choose 'Follow one particle' and watch the gold particle for three periods. Does it travel along with the wave, and how long does it take to return to the same place?
- Keep v = 1.0 m s⁻¹ and change f from 0.50 to 1.00 Hz. By what factor does λ change, and how many compressions fit in the row?
- Show the longitudinal wave with the s–x graph. Pause it and compare the position of a compression C with where s = 0. Where is the highest peak of the graph in the row of particles?
Common error: reading a displacement–position graph of a sound wave as a picture of the wave and putting compressions at the peaks; a compression sits where s = 0 and the graph slopes downwards, because the particles on either side are displaced towards it.